When A.D. comes to the home they heavily stage the house so in photographs it looks it's best. Just as if you were listing your home for sale you would need to de-clutter the space. People don't care about your personal photographs or other personal items. Even if you're proud of your art or a particular collection you might think twice about letting the world know what you own... I keep my personal photographs, memorabilia, and "stuff" out of view of most people on a daily basis.

I think that the wealthy who are included in AD have less crappy stuff. Their sense of style is why they are included in AD. Most wealthy have lots of crap accumulated over time. They have no better taste then less wealthy people.

I doubt that most of them actually have less stuff -- I expect that they probably have less stuff per square foot of living space.

This + Staging

It is not like they are taking pictures of the insides of your closets. If someone was going to take a picture of my place, I would do more than just "clean up"
I'd put away my fan even though it is a little warm in here...I'd stash my tennis racket even though I plan to use it again tomorrow. I would tidy up any project I was currently working on...but leave a few papers strewn "just so" on my desk or a bike part artfully disassembled on the work bench.

As for the size of the place...it can matter a lot. If I had another 500sq ft in my apartment, I would have some more stuff (a few pieces of furniture that I can think of) but I certainly wouldn't have double the possessions. Likewise, if I were in a 300sq ft studio I would lose a few things (downsize the furniture and drop some redundant items) but for the most part I would just figure out how to make my things fit...my out-of-season sporting goods and tools might end up under my bed instead of in a dedicated closet but I probably wouldn't toss things that I make regular use of.

I think a large measure of this is having a maid... not in the obvious sense, though.

Since I hired a maid, I find myself much less likely to keep things cluttered. On the one hand I sort of feel "bad" messing up the house, and on the other hand I know if I clutter things up it makes her job harder and irritates her

It's funny, in a way... having a maid at times makes ME feel like "the guest": she has her little flourished and way of doing things (for example, she arranges a tissue in a sort of origami rosette atop all the tissue boxes in the bathrooms, and she folds the towels in a certain complex, decorative way). I'll even sometimes reposition a statue or something, only to discover later that she's put it back in the "right place".

Now, I'm a complete pushover, obviously, but I suspect that wealthy folk are often somewhat beholden to their staff, in the same way we often are to our assistants (anyone who has ever had a really competent executive or personal assistant knows that sometimes it feels like they're more boss than employee).